Modal Symbolic Learning: Day 2¶

NATOPS: Interpretable gesture recognition¶

In [ ]:
using Pkg
Pkg.activate(".")
Pkg.instantiate()
Pkg.update()
Pkg.status()
  Activating project at `~/Desktop/modal-symbolic-learning-course`
    Updating registry at `~/.julia/registries/General`
    Updating git-repo `https://github.com/JuliaRegistries/General.git`
   Installed BenchmarkTools ───── v1.4.0
   Installed LoweredCodeUtils ─── v2.3.2
   Installed ModalDecisionTrees ─ v0.3.3
   Installed SoleLogics ───────── v0.6.11
   Installed SoleModels ───────── v0.5.3
    Updating `~/Desktop/modal-symbolic-learning-course/Project.toml`
  [e54bda2e] ↑ ModalDecisionTrees v0.3.2 ⇒ v0.3.3
  [b002da8f] ↑ SoleLogics v0.6.10 ⇒ v0.6.11
  [4249d9c7] ↑ SoleModels v0.5.2 ⇒ v0.5.3
    Updating `~/Desktop/modal-symbolic-learning-course/Manifest.toml`
  [6e4b80f9] ↑ BenchmarkTools v1.3.2 ⇒ v1.4.0
  [6f1432cf] ↑ LoweredCodeUtils v2.3.1 ⇒ v2.3.2
  [e54bda2e] ↑ ModalDecisionTrees v0.3.2 ⇒ v0.3.3
  [b002da8f] ↑ SoleLogics v0.6.10 ⇒ v0.6.11
  [4249d9c7] ↑ SoleModels v0.5.2 ⇒ v0.5.3
Precompiling project...
  ✓ BenchmarkTools
  ✓ LoweredCodeUtils
  ✓ Revise
  ✓ SoleLogics
  ✓ SoleModels
In [8]:
# Import libraries for statistics & Machine Learning
using Random
using DataFrames
using Plots
using StatsBase

using MLJ
using Sole
In [13]:
using JLD2
using DataFrames # (Maybe need version v1.6.1?)
JLD2.@load "COVID-dataset.jld2"
(X1_df, X2_df, y) = dataset;
In [9]:
countmap(y)
Out[9]:
Dict{String, Int64} with 2 entries:
  "POSITIVE" => 91
  "NEGATIVE" => 106
In [21]:
using SoleData

X_multimodal = MultiModalDataset([X1_df, X2_df])
Out[21]:
● MultiModalDataset{DataFrame}
   └─ dimensionalities: (1, 1)
- Modality 1 / 2
   └─ dimensionality: 1
197×30 SubDataFrame
 Row │ cough_F1                           cough_F2                           c ⋯
     │ SubArray…                          SubArray…                          S ⋯
─────┼──────────────────────────────────────────────────────────────────────────
   1 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [0.0658202, 0.0389503, 0.505408,…  [ ⋯
   2 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [1.62005, 0.648436, 0.248455, 0.…  [
   3 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [2.95991, 1.13398, 0.151934, 0.1…  [
   4 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [3.66094, 0.709991, 0.342895, 0.…  [
   5 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [1.26265, 0.966647, 0.281845, 0.…  [ ⋯
   6 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [4.12442, 2.09424, 0.267123, 0.1…  [
   7 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [3.42468, 1.26102, 0.164075, 0.0…  [
   8 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [10.8754, 0.646552, 0.395368, 0.…  [
   9 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [18.1984, 2.61893, 1.77536, 1.02…  [ ⋯
  10 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [3.37013, 1.19436, 0.97079, 0.60…  [
  11 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [2.34154, 0.925767, 0.378433, 0.…  [
  ⋮  │                 ⋮                                  ⋮                    ⋱
 188 │ [0.0726378, 0.00766837, 0.016578…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [
 189 │ [0.35084, 0.093121, 0.0471824, 0…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [ ⋯
 190 │ [0.00220116, 0.0199147, 0.166516…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [
 191 │ [0.0770436, 0.00820453, 0.001445…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [
 192 │ [0.0453022, 0.00469916, 0.001939…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [
 193 │ [3.23477e-5, 0.000132317, 0.0001…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [ ⋯
 194 │ [0.127782, 0.101379, 0.0369538, …  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [
 195 │ [0.00149723, 0.000397901, 0.0010…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [
 196 │ [0.00252365, 0.0540424, 0.065236…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [
 197 │ [0.115361, 0.0464483, 0.0123202,…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [ ⋯
                                                 28 columns and 176 rows omitted
- Modality 2 / 2
   └─ dimensionality: 1
197×30 SubDataFrame
 Row │ breath_F1                          breath_F2                          b ⋯
     │ Array…                             Array…                             A ⋯
─────┼──────────────────────────────────────────────────────────────────────────
   1 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [0.0275974, 0.123487, 0.954918, …  [ ⋯
   2 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [0.00551542, 0.738461, 1.23345, …  [
   3 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [0.0171132, 0.0128541, 0.175568,…  [
   4 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [0.0713483, 0.191903, 0.0599709,…  [
   5 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [0.0346951, 0.026089, 6.83611, 2…  [ ⋯
   6 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [0.0372815, 1.61098, 7.59596, 1.…  [
   7 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [0.0179035, 0.0158171, 6.72805, …  [
   8 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [0.038656, 0.202587, 0.0588298, …  [
   9 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [0.177666, 0.296219, 0.00581333,…  [ ⋯
  10 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [0.407654, 0.4168, 0.0640127, 0.…  [
  11 │ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [0.0442603, 0.0363921, 1.94756, …  [
  ⋮  │                 ⋮                                  ⋮                    ⋱
 188 │ [0.000519218, 0.000857345, 0.000…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [
 189 │ [0.0134826, 0.495593, 0.0, 0.0, …  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [ ⋯
 190 │ [0.000243355, 0.000393873, 0.000…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [
 191 │ [0.000504018, 0.00280926, 0.0030…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [
 192 │ [0.00447856, 0.0114002, 0.004106…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [
 193 │ [0.00081567, 0.00117782, 0.00106…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [ ⋯
 194 │ [0.101095, 0.472197, 0.0360748, …  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [
 195 │ [0.00159912, 0.00231749, 0.00020…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [
 196 │ [0.0280692, 0.0461481, 0.218395,…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [
 197 │ [0.251001, 0.0259159, 0.0174663,…  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0…  [ ⋯
                                                 28 columns and 176 rows omitted
In [23]:
modality(X_multimodal, 1) # Cough modality
Out[23]:
197×30 SubDataFrame
172 rows omitted
Rowcough_F1cough_F2cough_F3cough_F4cough_F5cough_F6cough_F7cough_F8cough_F9cough_F10cough_F11cough_F12cough_F13cough_F14cough_F15cough_F16cough_F17cough_F18cough_F19cough_F20cough_F21cough_F22cough_F23cough_F24cough_F25cough_F26cough_F27cough_F28cough_F29cough_F30
SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…SubArray…
1[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0658202, 0.0389503, 0.505408, 0.659653, 0.479911, 0.198311, 0.038341, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0130705, 0.00773471, 0.100364, 0.130993, 0.0953002, 0.0393805, 0.00761372, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00454093, 0.00181044, 0.00463918, 0.00812784, 0.0114677, 0.00279443, 0.00452539, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.44294, 0.176597, 0.452524, 0.792822, 1.11861, 0.27258, 0.441425, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.35527, 0.337327, 2.38008, 3.41855, 1.53125, 2.44285, 1.16185, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.45399, 0.207212, 0.596481, 0.796232, 2.05163, 0.889234, 0.912046, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][8.8225, 4.00392, 3.61966, 3.75479, 5.86163, 7.57988, 21.0325, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][68.6091, 57.6602, 42.1623, 22.0087, 44.1134, 183.205, 231.173, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][324.805, 251.949, 146.992, 89.8209, 1076.5, 1405.0, 521.713, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][529.788, 319.674, 3170.16, 8754.94, 12131.5, 2635.83, 160.221, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][135.031, 65.4094, 31734.0, 45007.7, 9341.06, 356.08, 348.502, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][277.601, 149.644, 6192.97, 6410.55, 526.879, 1016.61, 3058.69, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2463.94, 801.421, 218.482, 405.665, 5262.74, 5401.63, 1438.67, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][20281.1, 1322.6, 18382.4, 36321.8, 27790.6, 2262.41, 250.124, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][52706.7, 3379.9, 76705.7, 70649.4, 15600.4, 8659.85, 214.708, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][12469.4, 2027.9, 9573.34, 62751.8, 87979.5, 10106.8, 1175.91, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][5234.93, 3442.71, 27537.3, 49157.6, 34354.6, 7615.88, 590.886, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][10326.8, 8742.0, 29835.0, 65663.0, 37215.1, 9935.33, 1336.86, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][12937.2, 12652.3, 20925.7, 25481.2, 14228.1, 6209.21, 1830.89, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][15842.3, 11817.6, 20551.3, 66505.5, 53052.5, 15314.6, 4047.24, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][19539.8, 11725.6, 14110.9, 22741.0, 17571.2, 7866.31, 1784.98, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][7.47217e5, 2.85017e5, 1.91229e5, 161490.0, 74628.4, 5705.67, 230.46, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.82774e6, 1.12981e6, 6.8965e5, 5.55173e5, 2.28055e5, 11742.2, 526.767, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.8358e6, 8.47808e5, 3.64742e5, 3.14704e5, 1.72522e5, 31809.9, 4437.46, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][7.77569e5, 2.90888e5, 286646.0, 3.78292e5, 3.44293e5, 1.54095e5, 40524.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.94437e6, 1.92515e6, 9.28236e5, 2.59508e5, 68230.9, 40644.9, 7026.93, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.34059e6, 1.58093e6, 8.05443e5, 5.38573e5, 2.96582e5, 84622.9, 7822.09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
2[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.62005, 0.648436, 0.248455, 0.272204, 0.115829, 0.701655, 0.730142, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.321709, 0.128766, 0.0493379, 0.0540539, 0.0230012, 0.139334, 0.144991, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0714415, 0.0461039, 0.0216893, 0.0326628, 0.019149, 0.0363546, 0.0479683, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][6.96869, 4.49716, 2.11566, 3.18606, 1.86787, 3.54618, 4.67902, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][21.754, 27.4655, 19.0048, 24.0514, 5.83474, 28.537, 43.6516, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][34.8852, 51.9125, 36.1764, 19.2253, 2.13287, 35.007, 37.3961, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][234.05, 267.416, 167.449, 62.1158, 12.2897, 151.209, 164.396, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1454.56, 852.282, 446.942, 150.591, 88.5331, 443.756, 528.156, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][5123.56, 1131.67, 374.306, 911.971, 754.804, 356.213, 517.174, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][20084.3, 3480.32, 672.117, 10392.1, 9281.27, 898.532, 1178.98, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][15334.0, 5013.77, 1319.61, 5811.28, 5734.28, 2550.84, 2744.52, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][12234.9, 6993.57, 1761.05, 651.683, 2808.25, 2890.68, 3339.57, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][16674.7, 9460.58, 2878.9, 4119.18, 14762.8, 2806.11, 2028.18, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][56245.3, 21624.0, 6520.64, 41263.1, 63368.1, 7808.71, 4931.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][78468.2, 26281.8, 10982.8, 5368.62, 20602.4, 14850.2, 14849.9, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][77471.7, 95735.0, 16905.6, 8342.2, 14210.0, 9115.79, 12719.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][67572.1, 1.03941e5, 40420.4, 10467.9, 8491.01, 4898.5, 5365.45, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.55524e5, 2.6226e5, 1.04882e5, 18739.8, 12746.1, 7503.62, 8759.01, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.68154e5, 9.07885e5, 4.04412e5, 335687.0, 89441.4, 16392.0, 2126.91, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][6.92221e5, 6.03052e5, 1.1908e5, 58759.4, 31267.6, 5223.93, 1736.83, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][8.52602e5, 8.20567e5, 2.25646e5, 37287.0, 6070.59, 1029.12, 662.558, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.00165e6, 3.72761e6, 8.67491e5, 1.97835e5, 62275.3, 8543.62, 461.849, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.58505e6, 3.62319e6, 738156.0, 1.61754e5, 79843.7, 10647.7, 336.603, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][9.08381e6, 5.79745e6, 6.97654e5, 2.33825e5, 64936.9, 6078.8, 144.706, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.14781e7, 1.13822e7, 3.18543e6, 5.57376e5, 80210.4, 2854.2, 188.969, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.06059e7, 7.44956e6, 1.48442e6, 5.76729e5, 2.46594e5, 21856.1, 293.806, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.21352e6, 2.97859e6, 1.15466e6, 2.21273e5, 1.06559e5, 13745.5, 233.347, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
3[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.95991, 1.13398, 0.151934, 0.122773, 0.0847807, 0.0358195, 0.023554, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.587777, 0.225185, 0.0301709, 0.0243801, 0.0168357, 0.00711301, 0.00467733, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.287868, 0.100246, 0.00532329, 0.00555218, 0.00194837, 0.00139787, 0.0025744, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][28.0798, 9.77835, 0.519255, 0.541582, 0.190052, 0.136353, 0.251118, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][87.0256, 27.2477, 1.62891, 3.42497, 5.70717, 1.38103, 0.747201, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][26.205, 12.3015, 0.710897, 3.31912, 11.2409, 1.91642, 0.622233, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][104.305, 28.5733, 1.47273, 7.72693, 33.6984, 6.1959, 2.24012, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][787.131, 35.6819, 2.14433, 6.87128, 40.5095, 11.3619, 6.56239, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2810.15, 26.3572, 2.60753, 5.33105, 13.035, 15.2908, 14.1083, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1441.28, 70.0247, 4.71634, 55.6059, 144.928, 64.3011, 28.6293, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][310.68, 134.696, 6.17189, 77.5938, 548.601, 169.862, 26.9415, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4312.45, 430.115, 36.0941, 59.7097, 699.837, 515.62, 121.397, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][9462.69, 1239.38, 1889.39, 1715.57, 4571.37, 3039.89, 521.224, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][12799.2, 5572.2, 4783.39, 2921.7, 3869.14, 2904.15, 287.716, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][48185.1, 22933.0, 8947.61, 1410.66, 5173.81, 3749.97, 285.372, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][39728.7, 34053.4, 18530.0, 3214.0, 8251.46, 5393.83, 295.867, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][18179.9, 17902.9, 13901.1, 3031.17, 4455.63, 2813.3, 276.484, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][23039.8, 16723.5, 10761.6, 2520.38, 6145.44, 4647.94, 1075.16, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][23699.7, 24883.3, 25941.0, 19031.7, 63086.4, 65503.3, 6569.06, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][22270.5, 36373.6, 43627.6, 20155.9, 51197.1, 41757.6, 2081.54, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][7335.9, 7787.29, 6425.02, 1077.41, 5805.58, 5090.74, 565.701, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][12454.8, 61374.0, 37532.5, 3169.38, 17814.9, 17397.2, 1254.45, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][85598.0, 1.32e5, 77841.8, 10685.4, 62715.7, 62057.9, 3981.02, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.3401e5, 4.85673e5, 2.34642e5, 37125.9, 67977.1, 49896.6, 1859.31, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.76757e5, 3.1447e5, 2.0514e5, 47156.2, 29565.1, 12876.3, 314.342, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.85178e5, 41202.4, 25935.4, 9675.14, 12257.0, 7197.6, 409.98, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.87532e5, 1.68534e5, 1.27423e5, 25359.9, 10386.6, 3348.69, 403.783, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
4[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.66094, 0.709991, 0.342895, 0.265306, 0.0468018, 0.0975574, 0.0396136, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.726986, 0.140989, 0.0680918, 0.0526841, 0.00929385, 0.0193729, 0.00786644, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.596604, 0.143737, 0.0243013, 0.017446, 0.00756199, 0.00591798, 0.000982618, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][58.1952, 14.0207, 2.37045, 1.70176, 0.737627, 0.577263, 0.0958485, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][147.965, 47.2162, 6.6428, 5.11241, 2.9279, 8.16827, 2.79756, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][40.9492, 17.5678, 2.81489, 2.28017, 1.23771, 13.8401, 6.63218, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][87.6788, 41.5942, 7.84765, 8.43343, 3.92466, 37.327, 19.8962, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][358.114, 84.7886, 19.3406, 23.5386, 8.72719, 40.1797, 25.6276, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1598.58, 206.555, 34.0308, 26.9274, 7.90228, 10.7571, 13.6902, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1603.69, 353.238, 47.394, 21.8011, 5.74293, 109.841, 102.113, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1758.73, 496.494, 52.2081, 15.8906, 4.78958, 681.119, 554.578, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3664.62, 812.224, 50.6326, 67.4201, 43.7704, 334.839, 351.277, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][7484.34, 2693.82, 2067.11, 2069.21, 194.07, 590.997, 640.186, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][11556.3, 29918.0, 21582.0, 2577.26, 753.553, 2049.77, 2298.09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][30503.8, 28336.8, 13649.4, 5493.29, 3762.58, 4907.5, 5493.42, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][25393.4, 22818.6, 7584.81, 9041.14, 3711.21, 1887.35, 2093.86, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][34420.9, 1.18214e5, 94485.0, 19588.8, 3140.11, 3641.38, 2891.79, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][40911.6, 91877.1, 1.08737e5, 43639.5, 6988.58, 6171.03, 8560.34, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][64319.5, 93008.7, 71986.6, 31100.6, 9277.21, 28268.3, 41510.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][36343.9, 45441.8, 50437.0, 24456.9, 7994.68, 11499.8, 14622.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][31704.3, 10317.3, 7245.11, 4462.03, 1025.48, 1940.55, 3478.32, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][74359.6, 69897.9, 64846.6, 34381.0, 3091.71, 13139.2, 29797.8, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.78057e5, 3.32722e5, 1.90903e5, 87703.6, 15395.8, 64121.8, 1.12202e5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][7.02111e5, 8.22605e5, 6.52635e5, 2.68491e5, 26049.9, 45940.9, 64670.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.72789e5, 2.95965e5, 2.2296e5, 92396.7, 17608.2, 13774.1, 9150.45, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][364318.0, 2.32307e5, 93574.5, 16249.4, 3713.91, 1830.37, 1220.76, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.8397e5, 4.85444e5, 4.74261e5, 2.31186e5, 37388.0, 6486.39, 2700.48, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
5[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.26265, 0.966647, 0.281845, 0.14006, 0.0330181, 0.0189545, 0.0202496, 0.00427777, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.250736, 0.191956, 0.0559685, 0.027813, 0.00655671, 0.00376397, 0.00402115, 0.000849476, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.128993, 0.0764966, 0.0233883, 0.0117256, 0.00282783, 0.00201767, 0.00842082, 0.00644938, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][12.5825, 7.46179, 2.28138, 1.14377, 0.275838, 0.196811, 0.821401, 0.629098, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][39.6493, 29.8172, 6.77437, 4.26332, 1.11107, 0.975898, 4.93697, 3.74938, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][19.4749, 16.3886, 4.12483, 2.67541, 0.464519, 0.445975, 1.11086, 0.813915, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][51.152, 42.9527, 10.3997, 6.5627, 0.949258, 0.924119, 2.19942, 2.05453, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][111.898, 63.613, 17.1275, 8.80279, 1.06797, 0.925928, 4.48152, 7.07233, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][569.985, 108.755, 22.6375, 7.41687, 1.46129, 0.643923, 12.8904, 17.9929, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3222.3, 288.182, 23.4452, 12.9812, 3.44978, 1.28711, 10.3539, 15.2015, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1335.78, 165.667, 30.1376, 19.7937, 21.5971, 6.51968, 13.4725, 16.0345, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][777.711, 324.876, 109.027, 41.0903, 36.397, 20.945, 14.2237, 17.5114, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][10828.7, 1668.78, 323.53, 239.753, 539.395, 350.217, 87.928, 47.3984, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][78474.6, 39717.9, 5171.09, 5031.24, 7465.97, 1017.16, 471.802, 84.2813, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][57288.9, 58937.8, 63179.9, 41833.8, 10112.4, 2065.01, 179.165, 129.782, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][23679.4, 12135.6, 4153.62, 2523.42, 3794.78, 2171.68, 95.8407, 44.9481, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][40812.2, 67968.1, 46090.7, 37924.2, 35747.9, 12381.9, 493.346, 127.652, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][47647.5, 94273.0, 123220.0, 2.08642e5, 1.44458e5, 13063.8, 708.991, 314.243, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][56176.9, 1.60908e5, 2.16831e5, 226223.0, 1.06068e5, 3124.26, 348.297, 267.814, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][17601.5, 13799.6, 8708.93, 13248.8, 15733.6, 1562.7, 172.311, 125.331, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][30268.5, 6329.52, 2926.14, 4592.41, 3606.03, 1299.82, 173.137, 109.924, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.4524e5, 97346.0, 77712.2, 66049.1, 32499.9, 2262.61, 255.482, 134.958, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.45041e5, 1.85927e5, 1.45862e5, 1.00064e5, 49656.9, 9471.9, 514.132, 164.417, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.28999e6, 1.78603e6, 9.06583e5, 361846.0, 1.48162e5, 21636.4, 813.163, 287.636, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.107e5, 4.77255e5, 3.0263e5, 251105.0, 1.34015e5, 9386.39, 958.033, 412.196, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.25589e5, 2.59251e5, 1.49e5, 82328.3, 33612.5, 4056.65, 366.101, 145.276, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][6.30103e5, 265040.0, 2.20978e5, 1.96787e5, 1.01931e5, 9350.2, 658.859, 225.53, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
6[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.12442, 2.09424, 0.267123, 0.100803, 0.104586, 0.0637793, 0.0165705, 0.0220245, 0.0118193, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.819024, 0.415873, 0.053045, 0.0200174, 0.0207686, 0.0126652, 0.00329055, 0.0043736, 0.00234707, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.164946, 0.138568, 0.0176139, 0.00586853, 0.00260732, 0.00219175, 0.00100813, 0.00768144, 0.00797681, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][16.0895, 13.5165, 1.71813, 0.57244, 0.254329, 0.213792, 0.098337, 0.749279, 0.77809, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][57.5249, 64.2665, 7.79954, 1.9698, 0.330483, 0.45226, 0.217372, 6.69824, 10.3149, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][37.474, 59.5281, 4.7503, 0.659405, 0.174144, 0.141502, 0.0938198, 2.1568, 3.77767, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][107.032, 151.385, 12.9366, 1.88091, 0.404358, 0.235533, 0.168757, 3.21566, 5.71865, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][548.693, 237.948, 29.5336, 4.02686, 0.844208, 0.354745, 0.15178, 2.55989, 6.78283, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2463.97, 330.704, 74.9636, 6.15655, 2.28174, 0.791576, 0.144024, 10.3082, 31.518, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2521.94, 275.35, 62.0772, 7.09016, 6.20927, 2.49042, 0.441401, 25.592, 59.3716, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2283.88, 163.17, 34.8002, 12.7828, 11.1362, 4.36367, 1.87648, 13.4674, 34.1198, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2423.47, 316.186, 41.6317, 14.0202, 8.83124, 27.444, 35.1598, 11.1249, 20.4453, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4896.9, 1194.94, 141.845, 73.2266, 189.816, 1616.86, 1281.89, 111.627, 228.919, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][16370.4, 53892.8, 31325.2, 15457.8, 38633.8, 28463.0, 2135.17, 563.924, 473.507, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][56994.3, 62349.8, 1.41316e5, 96280.2, 24465.6, 4150.17, 3483.72, 2308.3, 1062.69, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][63242.7, 27907.8, 15871.4, 8175.98, 7403.91, 10243.8, 7056.21, 767.256, 662.359, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][89917.2, 1.79545e5, 2.1285e5, 166836.0, 89289.8, 58526.4, 15028.6, 1083.63, 608.261, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][82062.9, 2.7428e5, 3.06937e5, 2.76474e5, 2.14057e5, 1.31216e5, 32046.7, 1376.08, 1827.76, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][51484.9, 1.67269e5, 3.73738e5, 3.97781e5, 2.5919e5, 80968.7, 8583.49, 1459.11, 2839.03, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][23791.3, 47758.5, 42758.4, 31905.3, 33631.4, 34242.3, 4735.15, 1038.01, 1082.02, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][32387.5, 17823.1, 30922.7, 32287.6, 19238.6, 8375.24, 3255.07, 610.003, 463.91, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.29679e5, 2.11108e5, 1.85085e5, 83498.9, 98046.1, 55289.6, 9548.35, 1414.39, 973.205, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][373978.0, 3.00558e5, 230963.0, 2.28333e5, 2.63043e5, 1.62973e5, 31908.9, 3478.31, 4331.44, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.33111e6, 1.36412e6, 1.23544e6, 1.07179e6, 8.83399e5, 6.24532e5, 1.66885e5, 6095.3, 5996.45, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.05553e6, 7.40656e5, 9.20393e5, 8.56901e5, 6.08382e5, 3.30135e5, 85548.4, 8675.4, 4686.9, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.44999e5, 3.11548e5, 4.63817e5, 3.99629e5, 2.55266e5, 2.01334e5, 36326.3, 4568.45, 1253.19, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.71167e6, 1.342e5, 1.67066e5, 177223.0, 1.14439e5, 56836.7, 12498.7, 1993.0, 762.403, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
7[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.42468, 1.26102, 0.164075, 0.0827096, 0.0727358, 0.0332375, 0.00864315, 0.0294517, 0.0301729, 0.0451799, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.680069, 0.250411, 0.0325819, 0.0164244, 0.0144438, 0.00660026, 0.00171635, 0.00584848, 0.00599171, 0.00897178, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.201791, 0.102281, 0.0150567, 0.00414152, 0.00349754, 0.00190844, 0.000577779, 0.000441292, 0.00100831, 0.00227998, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][19.6835, 9.97687, 1.46869, 0.403981, 0.341164, 0.186157, 0.0563589, 0.0430454, 0.0983545, 0.222398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][49.073, 31.0425, 8.50607, 2.2064, 0.67495, 0.404055, 0.080384, 1.94059, 3.11224, 2.12355, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][52.2821, 42.5204, 5.05506, 1.43437, 0.239178, 0.190528, 0.0306607, 4.76722, 6.59105, 2.04922, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][172.223, 120.838, 12.1458, 3.88643, 0.636315, 0.561536, 0.0816999, 14.2693, 17.9649, 4.42329, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][438.032, 185.586, 23.712, 8.28798, 1.54169, 1.26043, 0.133984, 17.1077, 19.7193, 4.58966, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][924.48, 147.008, 39.0836, 11.0064, 2.65456, 1.69573, 0.148915, 3.81685, 7.39805, 7.47142, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2184.51, 310.218, 93.9812, 12.194, 2.87499, 2.17631, 0.688324, 24.6385, 58.2586, 16.1209, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1597.04, 422.866, 104.443, 16.1897, 5.57772, 3.96736, 1.85136, 195.327, 284.368, 31.6101, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1328.28, 463.92, 126.573, 15.3028, 13.2119, 9.71817, 7.4392, 66.6225, 99.192, 38.3469, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3160.3, 978.408, 202.802, 39.8813, 38.4745, 97.7278, 306.249, 408.966, 493.164, 209.307, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][28653.6, 17415.3, 899.982, 221.43, 522.198, 1991.81, 3082.06, 1361.55, 2094.92, 593.447, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][16942.1, 36064.2, 23303.5, 14480.2, 25258.4, 12677.8, 3292.91, 3858.24, 3715.01, 544.271, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][15202.9, 15073.4, 5682.16, 5509.79, 3588.41, 1198.06, 2217.13, 1475.32, 927.36, 291.582, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][19801.3, 58589.3, 52024.2, 42651.3, 21346.6, 12868.5, 9942.05, 2250.63, 2153.4, 494.597, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][27283.4, 71762.8, 74700.7, 53552.8, 33752.2, 33638.5, 19547.6, 5892.04, 9650.07, 3241.56, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][60282.3, 106667.0, 1.92593e5, 2.73614e5, 2.6819e5, 172022.0, 41449.1, 13286.6, 24033.3, 5794.77, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][70190.1, 22550.6, 6916.46, 7129.64, 8742.1, 11957.5, 10555.3, 3342.87, 3796.32, 1656.02, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][38128.5, 10349.8, 4832.47, 9184.08, 10703.4, 6471.21, 2614.78, 1621.49, 4393.34, 3064.31, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][83477.0, 47135.2, 25527.8, 25670.9, 30235.8, 27854.9, 9323.31, 7297.68, 16519.4, 7006.36, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.22372e5, 1.014e5, 87109.2, 73837.1, 97165.1, 68035.1, 22994.4, 31337.5, 82626.4, 19052.4, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.00222e5, 4.58337e5, 4.08592e5, 2.94701e5, 2.43381e5, 1.58678e5, 59393.1, 26546.3, 44458.0, 6444.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.75489e5, 4.96473e5, 6.06817e5, 5.50561e5, 4.60877e5, 4.30587e5, 1.25109e5, 18205.0, 5687.05, 749.453, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.31253e5, 1.45413e5, 1.4628e5, 1.44849e5, 74441.9, 38992.0, 12076.2, 2246.5, 468.582, 156.219, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.44753e5, 241190.0, 3.1205e5, 447032.0, 3.64429e5, 269564.0, 71915.6, 7123.12, 2363.88, 275.769, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
8[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][10.8754, 0.646552, 0.395368, 0.306463, 0.0464313, 0.0182149, 0.0898324, 0.11998, 0.025443, 0.011258, 0.0263648, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.15962, 0.128392, 0.0785118, 0.0608572, 0.00922028, 0.00361709, 0.0178388, 0.0238254, 0.00505245, 0.00223559, 0.00523549, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.531624, 0.0291421, 0.0249703, 0.0202988, 0.00218111, 0.00111567, 0.00265106, 0.00404789, 0.00576916, 0.00679558, 0.00494477, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][51.8568, 2.84264, 2.4357, 1.98003, 0.212754, 0.108827, 0.258595, 0.394848, 0.562747, 0.662868, 0.482333, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][60.9472, 9.82345, 5.82059, 4.4568, 0.429483, 0.32841, 7.61417, 14.7855, 7.71569, 3.51884, 1.01496, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][22.8551, 13.8948, 4.33122, 3.00244, 0.296515, 0.142112, 10.9202, 20.4616, 4.59051, 0.81392, 0.470563, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][158.491, 42.6918, 17.3141, 9.99483, 0.883501, 0.353452, 26.4952, 44.6971, 8.99552, 4.02561, 3.29044, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1234.27, 85.7787, 46.9912, 19.7734, 2.45632, 0.571253, 24.8288, 36.7208, 22.6779, 23.5594, 11.8309, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3307.82, 103.749, 48.9804, 17.3767, 5.47667, 0.733437, 21.9688, 88.8222, 150.572, 56.0259, 10.645, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3201.91, 233.555, 52.246, 20.8436, 12.7354, 1.99009, 252.669, 894.461, 388.302, 32.8036, 20.5925, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3635.19, 237.362, 70.0679, 24.073, 18.8189, 1.59053, 359.945, 671.977, 78.7436, 10.7343, 8.97029, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4083.96, 211.063, 116.868, 64.5978, 66.6072, 30.6471, 133.206, 374.632, 115.298, 36.1098, 6.41714, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][5643.76, 817.773, 171.385, 918.249, 1282.73, 313.279, 777.217, 1347.91, 413.508, 76.4081, 4.10891, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][19746.7, 33892.9, 24858.9, 18318.7, 4581.04, 1319.23, 1939.42, 3012.32, 586.096, 31.2144, 4.22038, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][54910.6, 38309.5, 27922.5, 7712.53, 2414.21, 3601.04, 2176.04, 1919.0, 277.793, 9.77935, 3.04255, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.0129e5, 27810.5, 14630.8, 12346.3, 11584.7, 6478.55, 1207.08, 1099.74, 146.58, 5.94628, 1.71999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][98255.5, 1.52647e5, 97560.2, 53511.8, 22040.3, 4715.55, 1101.36, 1187.15, 152.923, 10.6421, 2.28049, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][83419.1, 2.91822e5, 1.71942e5, 79663.4, 39292.1, 5125.42, 1751.86, 2632.0, 668.424, 84.5324, 10.3401, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][21282.7, 41021.4, 61095.0, 57024.5, 19842.9, 6214.83, 4623.51, 5466.86, 1058.01, 120.311, 25.2199, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][29744.2, 35597.1, 35376.6, 22575.2, 18395.7, 6131.97, 1172.74, 1340.57, 307.195, 79.0653, 22.0758, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.03124e5, 1.52317e5, 61250.5, 14879.8, 3890.83, 1263.43, 221.818, 245.358, 71.4148, 31.6592, 14.4644, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][5.18427e5, 4.25194e5, 4.75416e5, 3.6324e5, 1.44266e5, 13659.7, 1829.72, 2162.35, 564.955, 48.1775, 17.1197, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][7.12858e5, 1.06315e6, 7.28298e5, 3.45826e5, 1.99908e5, 54517.0, 5310.46, 6553.6, 1710.12, 86.5629, 22.3082, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.16241e6, 4.6001e6, 3.94375e6, 1.81217e6, 5.94729e5, 59782.2, 6102.24, 7774.32, 2267.04, 194.698, 57.6554, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.62278e6, 7.34011e5, 4.5979e5, 3.56661e5, 1.47656e5, 34913.7, 2757.37, 4206.49, 1498.93, 216.208, 80.0921, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.4782e6, 3.43834e5, 1.73423e5, 95849.5, 57655.0, 20233.9, 2617.48, 3240.86, 1015.35, 330.658, 176.518, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.79891e6, 7.07743e5, 8.90214e5, 1.13672e6, 7.18273e5, 1.3446e5, 11547.2, 5675.67, 508.817, 91.5365, 57.5119, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
9[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][18.1984, 2.61893, 1.77536, 1.02094, 0.197965, 0.506792, 0.250556, 0.112402, 0.234197, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.61381, 0.520065, 0.35255, 0.202737, 0.0393117, 0.100638, 0.0497552, 0.0223206, 0.0465066, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.0694, 0.227274, 0.472316, 0.224377, 0.0118801, 0.0112027, 0.0299956, 0.0321187, 0.027308, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][104.313, 22.1692, 46.0716, 21.8866, 1.15883, 1.09276, 2.92589, 3.13299, 2.66373, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][319.638, 114.507, 216.95, 64.5679, 27.125, 146.721, 95.0245, 9.53057, 3.57577, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][175.66, 80.3852, 62.5621, 11.9524, 30.0728, 220.546, 117.534, 4.27698, 4.56987, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][514.919, 198.581, 127.4, 18.3973, 65.5414, 489.872, 258.321, 19.7452, 12.5356, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2290.12, 281.493, 136.406, 12.2952, 41.3891, 306.936, 203.44, 73.8918, 19.0718, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4791.14, 299.539, 143.842, 16.3087, 18.8866, 135.072, 244.927, 100.706, 26.8707, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2419.8, 241.673, 173.338, 26.1446, 298.465, 2012.8, 1261.25, 102.711, 34.225, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1081.7, 171.006, 130.206, 41.5457, 286.378, 1611.0, 533.597, 96.4571, 18.9268, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2207.56, 408.005, 292.076, 143.191, 137.129, 1042.24, 642.64, 83.8508, 10.0131, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][5792.86, 853.378, 1174.48, 1202.43, 1010.33, 4519.14, 2762.95, 146.459, 8.22149, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][19975.3, 12226.5, 12692.1, 11734.6, 3892.55, 17111.8, 9868.28, 141.957, 9.27232, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][47040.4, 84614.7, 70066.2, 24383.5, 1892.47, 22516.3, 13751.2, 90.4159, 4.75663, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][19515.0, 9192.67, 8285.14, 1612.57, 2541.5, 12473.9, 5664.58, 139.223, 4.78841, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][23468.0, 9017.16, 11540.4, 13127.3, 5868.78, 16339.9, 5246.34, 151.649, 8.4468, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][68508.2, 94404.5, 65298.5, 28851.0, 4533.38, 43905.3, 26444.5, 886.703, 71.4924, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.04067e5, 1.20649e5, 98515.3, 27660.9, 15783.7, 1.79131e5, 1.19305e5, 4720.23, 745.261, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.796e5, 1.31627e5, 71817.3, 33551.8, 9946.91, 61920.1, 34266.1, 2154.26, 892.119, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.48489e5, 19126.0, 13381.3, 4352.72, 1802.53, 16875.0, 13420.7, 987.673, 359.928, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][67652.6, 19875.6, 17713.7, 5892.83, 2031.66, 10815.3, 7635.95, 746.118, 377.998, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][78840.1, 52566.4, 56656.8, 22002.1, 2847.44, 10092.7, 7801.78, 405.978, 73.0752, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.11847e5, 406885.0, 3.10409e5, 96114.1, 14839.7, 72819.4, 47785.6, 1716.9, 382.843, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.91813e6, 7.04341e5, 3.79502e5, 1.29916e5, 28547.8, 35280.9, 7633.73, 206.455, 92.1204, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.19054e6, 6.44997e5, 2.51258e5, 75966.9, 17468.2, 11109.2, 2663.06, 113.218, 52.4331, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.38328e6, 3.71488e5, 2.06183e5, 82574.7, 25704.6, 15146.7, 2636.3, 110.028, 53.8018, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
10[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.37013, 1.19436, 0.97079, 0.600305, 0.176715, 0.0773258, 0.0182055, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.669236, 0.237175, 0.192778, 0.119208, 0.0350919, 0.0153553, 0.00361524, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.446583, 0.20182, 0.068445, 0.0334676, 0.0137318, 0.00983118, 0.00542909, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][43.5615, 19.6863, 6.6764, 3.26457, 1.33945, 0.958973, 0.529576, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][156.355, 68.3481, 19.5355, 9.7452, 19.7202, 34.0038, 4.53388, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][66.141, 21.6009, 9.70487, 3.89796, 20.7443, 34.8802, 2.44411, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][294.463, 62.8391, 28.09, 11.3367, 46.0355, 71.1349, 5.46733, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][891.481, 157.743, 62.8578, 31.4354, 38.1107, 42.9304, 11.1868, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2352.51, 365.704, 95.5167, 49.7098, 24.0039, 48.7936, 25.1504, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][8246.09, 967.78, 155.305, 47.334, 291.603, 534.511, 67.0029, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][6024.03, 1189.12, 265.899, 56.1783, 266.784, 384.745, 171.963, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3533.57, 1226.86, 287.814, 107.679, 76.4183, 117.665, 74.5026, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][17523.0, 7519.97, 2077.73, 284.892, 134.043, 221.827, 76.6903, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][45841.8, 30133.3, 13270.2, 5192.14, 573.511, 1364.3, 588.844, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][92531.6, 21482.3, 22825.5, 8430.95, 1080.04, 4441.88, 2314.94, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][54982.9, 29508.2, 17050.0, 1898.75, 2338.2, 4518.82, 680.442, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][71814.8, 89066.3, 25261.9, 2756.71, 944.552, 1880.57, 521.817, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][60571.1, 89317.5, 60506.8, 8202.06, 2781.65, 6776.13, 2259.45, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][70759.6, 82738.4, 46046.0, 5315.16, 4730.53, 11924.1, 3320.59, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][78538.9, 43817.4, 24255.7, 3411.18, 3133.98, 5237.83, 1218.67, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][97326.6, 22813.3, 14944.5, 3651.76, 2013.17, 3132.29, 1212.68, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.23273e5, 1.14776e5, 82447.6, 10985.9, 2914.84, 5551.98, 2231.11, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.77328e5, 2.11186e5, 132127.0, 20059.1, 6631.32, 7568.12, 2523.18, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][6.38947e5, 5.47384e5, 3.78993e5, 22361.1, 3761.69, 5458.03, 2191.26, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][6.10758e5, 3.41778e5, 1.82234e5, 18213.7, 7352.09, 8288.47, 1414.14, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.19789e5, 2.57071e5, 1.15207e5, 17495.7, 3363.3, 2429.97, 443.019, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][674707.0, 4.4471e5, 1.95013e5, 34913.7, 7769.58, 4178.22, 338.683, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
11[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.34154, 0.925767, 0.378433, 0.123683, 0.0554886, 0.0348641, 0.0349075, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.464981, 0.183838, 0.0751489, 0.0245608, 0.0110189, 0.00692327, 0.0069319, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.388725, 0.139274, 0.0471144, 0.0156152, 0.0121435, 0.0237099, 0.0155309, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][37.9178, 13.5853, 4.59573, 1.52317, 1.18452, 2.31276, 1.51494, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][217.601, 77.2663, 10.8263, 6.32299, 13.4739, 31.2038, 9.66738, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][106.796, 32.4735, 5.26017, 2.09609, 5.57463, 12.6613, 2.43583, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][277.033, 64.1409, 11.2031, 4.36364, 8.79765, 18.0226, 4.11183, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][999.644, 81.9154, 13.4892, 5.16238, 5.41049, 12.1697, 12.3495, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2400.27, 87.6089, 17.6806, 4.22724, 7.004, 50.1794, 36.2726, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2639.01, 194.706, 34.3255, 10.1684, 14.6814, 84.9472, 27.6049, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2106.86, 301.505, 53.3498, 16.7153, 15.2046, 30.8032, 11.4269, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1423.65, 362.226, 43.7223, 20.82, 31.2697, 71.514, 48.2697, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2722.88, 817.225, 132.639, 197.576, 143.617, 164.932, 130.755, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][25460.9, 4361.11, 4820.59, 3457.14, 356.896, 232.836, 167.751, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][51125.5, 47000.3, 17446.0, 1250.98, 207.364, 574.049, 294.856, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][80356.0, 9525.29, 1177.41, 763.166, 729.577, 643.218, 193.964, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][41449.3, 7972.57, 4625.34, 3406.24, 352.905, 396.441, 214.448, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][59798.9, 42373.6, 17077.1, 2659.07, 345.079, 1190.74, 996.585, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.04703e5, 91496.9, 11170.0, 3893.02, 1574.94, 2627.33, 1684.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][61889.9, 10436.1, 3856.79, 1454.4, 1088.22, 1116.16, 535.533, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][24234.8, 2942.63, 1284.6, 289.374, 168.726, 254.392, 177.22, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.12408e5, 21933.1, 9727.37, 1733.79, 437.41, 825.012, 309.154, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.04032e5, 49172.9, 25588.7, 7479.12, 1876.08, 1661.48, 666.537, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][784536.0, 3.04213e5, 1.13671e5, 21546.3, 4499.85, 2484.3, 1116.24, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.09377e6, 6.04365e5, 2.83506e5, 68889.4, 17995.0, 18668.1, 8841.47, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.6458e6, 6.22042e5, 2.81978e5, 65010.7, 12437.2, 8176.51, 2151.71, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][253010.0, 66991.3, 25185.6, 7200.73, 2197.7, 1289.79, 449.488, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
12[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.07298, 2.57072, 0.687283, 0.322323, 0.214695, 0.0641531, 0.0246654, 0.0356907, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.61023, 0.510491, 0.13648, 0.0640066, 0.0426338, 0.0127395, 0.00489802, 0.00708743, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.204552, 0.231794, 0.051393, 0.0287529, 0.0233669, 0.00844628, 0.00442164, 0.00340762, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][19.9528, 22.6101, 5.01308, 2.80468, 2.27931, 0.823884, 0.431304, 0.332393, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][75.7704, 65.3334, 10.8787, 6.68328, 39.0807, 17.2155, 1.48772, 0.433085, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][85.5894, 46.8714, 3.23801, 2.35077, 27.7438, 12.7074, 0.313934, 0.394331, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][482.028, 127.0, 12.7559, 5.77321, 47.7432, 22.6437, 2.13238, 1.44283, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2864.31, 239.924, 46.5537, 8.46633, 28.6383, 27.855, 14.3802, 3.16736, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][5418.38, 252.033, 49.7085, 12.1586, 78.9562, 98.4969, 29.3789, 6.39385, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1941.13, 474.993, 39.41, 19.0993, 368.63, 219.226, 36.7584, 16.67, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1568.86, 603.34, 40.1766, 11.4549, 110.336, 109.271, 62.0838, 27.2405, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1490.5, 383.782, 55.6588, 16.121, 104.094, 90.6794, 63.1952, 42.7605, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2559.54, 410.284, 122.797, 36.1423, 469.858, 333.973, 122.41, 72.8257, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][14168.3, 672.405, 99.8046, 88.484, 1503.26, 1371.22, 366.758, 104.775, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][51757.4, 1222.96, 102.75, 262.084, 3539.11, 4070.57, 499.431, 90.2152, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][22181.9, 1796.59, 196.855, 442.556, 3415.11, 1717.36, 135.926, 31.1462, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][33665.6, 16849.0, 4569.12, 1640.58, 2192.02, 1568.63, 203.892, 46.781, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][40277.0, 29092.3, 12903.3, 1254.84, 5150.63, 4957.78, 1353.79, 397.302, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][64674.9, 19832.0, 4520.22, 1743.34, 14492.1, 15797.4, 3462.22, 550.115, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][66666.6, 2453.63, 583.168, 579.314, 2588.16, 2377.38, 676.225, 167.056, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][76701.9, 2966.63, 618.305, 422.079, 1663.13, 1707.88, 745.378, 320.232, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.77635e5, 11485.5, 2535.62, 1375.23, 4137.03, 3490.8, 731.529, 215.071, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.9469e5, 30881.1, 18810.2, 5159.56, 9893.79, 8561.0, 1606.42, 419.461, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][792515.0, 59472.9, 27191.6, 6990.04, 7554.09, 8188.63, 3081.72, 1442.57, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][5.27641e5, 86196.2, 46352.5, 21304.0, 19972.1, 6194.02, 3036.64, 1981.62, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.331e6, 93031.1, 34402.6, 12832.2, 9110.71, 3529.93, 675.309, 230.184, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.92566e5, 41036.7, 25526.5, 8916.29, 11981.5, 4253.0, 453.673, 173.776, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
13[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.77748, 0.796787, 0.0738923, 0.0442614, 0.0555183, 0.0385192, 0.0508226, 0.101736, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.352971, 0.158225, 0.0146735, 0.00878938, 0.0110248, 0.0076491, 0.0100923, 0.0202027, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.203237, 0.0634473, 0.00590952, 0.00739434, 0.0543729, 0.0397721, 0.0168973, 0.0131004, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][19.8246, 6.1889, 0.576438, 0.721273, 5.30375, 3.87953, 1.64823, 1.27787, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][124.634, 54.834, 2.34781, 2.41349, 40.6377, 23.3851, 3.94196, 1.50084, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][186.581, 65.7612, 2.12284, 0.663678, 11.2329, 5.3498, 0.707124, 0.730327, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][704.364, 148.441, 5.73875, 1.69698, 15.755, 11.4785, 4.47877, 3.11821, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2321.02, 133.551, 7.94585, 2.78301, 22.3367, 44.4627, 18.6896, 7.98156, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2514.79, 41.9798, 5.11629, 2.87657, 104.26, 128.672, 27.8394, 24.7023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1209.35, 111.5, 7.05355, 7.63288, 108.886, 87.4096, 54.1756, 56.6978, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1087.4, 86.65, 5.31522, 7.86358, 46.7023, 19.3707, 18.692, 9.42548, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1095.46, 43.8612, 4.47532, 7.27559, 90.0504, 95.3982, 46.992, 23.5355, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][5313.41, 98.9343, 5.80101, 20.4876, 538.687, 481.1, 178.959, 27.1045, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][52939.2, 182.635, 24.9805, 46.2887, 535.117, 418.2, 154.758, 13.453, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][63418.5, 317.791, 101.497, 253.755, 2012.01, 1969.08, 242.854, 13.0324, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][25400.0, 844.502, 2453.88, 2756.33, 1992.17, 926.157, 198.911, 14.63, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][43050.9, 13510.0, 8776.78, 2580.14, 1100.79, 689.201, 244.525, 21.4951, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][32548.9, 10756.9, 2708.59, 396.899, 1883.98, 2075.85, 700.733, 74.3869, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][49564.7, 1816.13, 950.232, 1144.21, 5622.47, 2581.87, 1350.99, 317.29, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][35322.3, 2213.58, 1094.95, 1597.92, 5503.05, 3409.37, 1128.94, 376.748, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][23695.3, 1530.78, 284.107, 181.767, 696.674, 723.757, 327.421, 132.597, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.50965e5, 6586.02, 1725.3, 1047.81, 1947.87, 1762.02, 579.249, 188.906, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.22333e5, 13705.6, 7470.78, 3432.98, 3172.74, 2108.98, 419.699, 87.7327, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.06682e6, 1.3009e5, 58963.0, 9291.6, 4988.88, 3195.24, 708.604, 118.306, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.17282e6, 1.21511e5, 68782.6, 19980.3, 11376.4, 6650.9, 806.036, 138.297, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][5.32616e5, 38504.2, 18766.0, 7171.64, 6999.12, 3885.44, 474.652, 143.486, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.15976e6, 66152.8, 21711.5, 6822.59, 10863.9, 4850.65, 571.616, 216.577, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮
186[0.0174438, 0.00310092, 0.00849625, 0.026699, 0.0209502, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0132189, 0.00241784, 0.0035302, 0.00828464, 0.00804756, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00534833, 0.000978251, 0.00142831, 0.00335194, 0.00325602, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00761603, 0.00336311, 0.00303914, 0.0176728, 0.00857069, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00685904, 0.0030301, 0.00274326, 0.0159144, 0.007736, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.063674, 0.0279074, 0.0298889, 0.130429, 0.0989523, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0711588, 0.0281567, 0.0296447, 0.0901159, 0.0834384, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.191892, 0.134706, 0.0402976, 0.270762, 0.343598, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.924332, 0.977029, 0.841115, 1.50237, 2.78743, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][22.6832, 9.07198, 17.4938, 19.778, 27.2206, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][133.13, 22.4991, 145.724, 216.318, 137.163, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][251.369, 12.5201, 212.579, 1615.37, 687.172, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][454.676, 27.8568, 41.6125, 7433.74, 4648.45, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][292.397, 115.87, 158.062, 1159.76, 966.212, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][766.985, 282.466, 978.475, 1031.66, 682.515, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][5574.79, 3934.18, 5856.77, 13017.9, 3727.62, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][10504.4, 1131.58, 1335.97, 9885.21, 5373.02, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][15786.8, 2770.87, 3241.64, 12780.9, 2412.14, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][12599.6, 5966.12, 4462.94, 10123.4, 2109.77, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][11800.9, 9975.36, 9992.27, 9421.64, 4391.57, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][41242.4, 25335.9, 16439.9, 43828.2, 20822.6, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.64176e5, 90518.6, 10890.7, 11985.6, 3423.28, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.33637e5, 74169.5, 19976.8, 13575.9, 2001.45, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.88033e6, 7.10186e5, 1.77592e5, 1.35604e5, 25446.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.03456e6, 1.19725e6, 1.54486e5, 1.41498e5, 26203.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.72399e6, 1.27537e6, 1.5455e5, 1.32944e5, 23047.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.99741e6, 1.12252e6, 1.88817e5, 2.71814e5, 52557.7, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][6.89062e5, 2.29374e5, 1.43654e5, 1.13484e5, 16261.7, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
187[0.0291811, 0.0169011, 0.0162059, 0.0177519, 0.121101, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0421715, 0.00966519, 0.00904388, 0.0169365, 0.0497429, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0170625, 0.00391051, 0.00365913, 0.00685247, 0.0201259, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.181893, 0.0464096, 0.00634378, 0.0110066, 0.0522485, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.164498, 0.04206, 0.00570707, 0.00988836, 0.0481563, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.67007, 0.829326, 0.0319864, 0.0367413, 4.99969, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][5.11151, 0.850098, 0.0569604, 0.1121, 30.7308, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][16.5958, 0.855482, 0.156334, 0.519324, 129.415, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][36.268, 0.606582, 0.304205, 0.756828, 135.214, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][71.5685, 2.29434, 1.18257, 0.512215, 28.0198, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][81.8014, 32.9256, 18.5455, 3.25372, 174.747, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][134.567, 365.304, 250.695, 16.126, 530.572, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][182.355, 349.712, 201.699, 37.9573, 119.204, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1293.56, 735.043, 1669.64, 2641.95, 459.472, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][12848.8, 4812.97, 12542.7, 11533.4, 462.524, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][58893.1, 24212.2, 6446.18, 1336.32, 297.868, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][8009.08, 5459.35, 1346.01, 106.845, 37.4606, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4722.67, 3870.87, 1449.97, 470.779, 69.0678, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][29559.3, 1.07566e5, 1.09275e5, 7262.55, 4893.8, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.41214e5, 3.71867e5, 1.55983e5, 22517.7, 3425.55, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.55783e5, 109252.0, 33611.9, 5995.83, 951.081, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][90907.3, 95050.1, 31891.2, 6297.47, 1049.79, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][40828.2, 28222.7, 17116.0, 2650.0, 502.319, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.7979e5, 1.98252e5, 29279.1, 2475.27, 146.264, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.98778e5, 74616.2, 14847.6, 1496.66, 72.7096, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][19935.9, 14455.1, 6697.27, 1191.26, 62.9539, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][18396.3, 3995.76, 473.269, 43.6156, 92.2445, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][14823.7, 6247.5, 867.695, 92.6666, 145.434, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
188[0.0726378, 0.00766837, 0.016578, 0.0160573, 0.0146287, 0.011821, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0858145, 0.00341952, 0.00950763, 0.0234871, 0.0317684, 0.0292289, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0347203, 0.00138353, 0.00384676, 0.00950284, 0.0128534, 0.011826, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0374854, 0.00652354, 0.00951697, 0.0476727, 0.0741164, 0.033361, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0338942, 0.00592369, 0.00862781, 0.0430314, 0.0668577, 0.0300568, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.666805, 0.208233, 0.232384, 0.490413, 0.618556, 0.222889, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.69008, 0.782383, 0.70679, 0.753357, 0.735469, 0.466869, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][21.4386, 4.35686, 2.48301, 1.88091, 1.76483, 1.26077, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][54.3725, 13.1092, 11.078, 5.20239, 7.12761, 4.74615, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][129.17, 32.2144, 28.8786, 18.5183, 23.9582, 12.6332, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][309.495, 68.6928, 35.517, 24.8545, 25.0249, 10.3097, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][282.545, 103.92, 54.8907, 25.4878, 14.4915, 5.70231, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][896.839, 189.997, 102.044, 92.851, 43.8193, 10.3705, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1619.75, 362.102, 194.17, 162.506, 69.324, 15.6593, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2063.37, 530.477, 187.925, 217.947, 104.797, 36.4428, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3599.3, 459.729, 4799.39, 6558.91, 478.835, 142.955, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][9312.99, 8072.87, 20339.2, 18079.4, 697.515, 305.975, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][75884.5, 75614.6, 23103.4, 2621.56, 1000.07, 204.376, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][11059.6, 7511.45, 5473.34, 4496.68, 2654.2, 197.861, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][22521.9, 219088.0, 3.03695e5, 128710.0, 9088.88, 1023.89, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.42665e5, 6.04917e5, 7.16333e5, 3.43522e5, 13815.0, 2228.18, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][421529.0, 6.84435e5, 5.06518e5, 79203.1, 12049.3, 1825.16, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.77911e5, 2.71343e5, 96155.9, 46434.4, 18765.9, 1134.17, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.0588e6, 1.87371e6, 1.70024e6, 7.31651e5, 2.21438e5, 6702.24, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.51097e6, 665173.0, 2.26159e5, 1.42875e5, 79750.4, 4552.61, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.81988e6, 3.21523e5, 83547.6, 40930.4, 19155.0, 2516.82, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.19896e6, 9.51786e5, 7.64453e5, 5.83763e5, 1.89066e5, 5467.64, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.95484e6, 1.20665e6, 708663.0, 7.03012e5, 2.07506e5, 3703.53, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
189[0.35084, 0.093121, 0.0471824, 0.766623, 6.82305, 1.83248, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.204067, 0.0762902, 0.0502624, 0.666629, 5.60448, 1.80846, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.082565, 0.0308668, 0.020336, 0.269717, 2.26756, 0.731699, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.327706, 0.0746536, 0.0609227, 0.206968, 8.34425, 4.18508, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.295509, 0.067075, 0.0551633, 0.187895, 7.54198, 3.77299, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.14115, 0.301486, 1.71981, 7.4684, 101.304, 35.4741, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][10.6782, 0.488366, 11.1674, 118.74, 177.465, 28.9003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][56.6589, 3.79526, 58.9, 781.867, 538.663, 35.1794, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][361.71, 34.7833, 109.088, 1256.37, 627.572, 27.8791, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1401.89, 72.0948, 56.5619, 307.354, 156.284, 37.5202, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1877.3, 51.3806, 29.7751, 183.572, 424.245, 60.9739, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][399.433, 10.9505, 18.5816, 1918.96, 1830.02, 91.5303, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][180.233, 4.29405, 19.9826, 693.545, 365.067, 28.5908, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][162.37, 8.9414, 45.0704, 611.088, 426.586, 15.7868, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1121.79, 155.525, 721.171, 1435.29, 1108.54, 107.356, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2339.34, 2285.91, 4256.77, 2044.67, 1457.53, 153.644, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][15965.4, 13701.6, 1472.37, 470.131, 199.032, 65.0501, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][11569.5, 11300.4, 716.581, 627.936, 367.873, 34.95, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][767.553, 556.328, 381.932, 234.665, 280.954, 50.2157, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][12522.1, 23402.7, 21136.7, 3011.0, 1820.55, 386.806, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][41116.4, 96147.7, 42650.0, 5573.06, 1548.79, 660.962, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][6440.43, 3523.66, 1235.28, 416.587, 272.719, 73.6723, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][60090.9, 77395.2, 8728.88, 4050.68, 1886.54, 271.188, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][77705.5, 42450.3, 14884.8, 6831.3, 4543.65, 613.393, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.41254e5, 21558.0, 9203.0, 5968.01, 3919.22, 632.27, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.02391e5, 49248.4, 25120.9, 13453.8, 6116.37, 985.465, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.69599e5, 2.91408e5, 1.32637e5, 62097.5, 31612.4, 4341.53, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.10349e6, 6.50353e5, 3.85949e5, 1.59593e5, 78847.9, 9034.49, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
190[0.00220116, 0.0199147, 0.166516, 0.0951876, 0.128625, 0.459631, 0.263766, 0.0405767, 2.5724, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00105089, 0.0269954, 0.201371, 0.124756, 0.0703357, 0.288238, 0.229707, 0.0601887, 3.26771, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.000425188, 0.0109223, 0.0814741, 0.0504759, 0.0284576, 0.11662, 0.0929391, 0.0243522, 1.32211, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00057181, 0.019619, 0.250694, 0.156108, 0.335901, 1.76911, 1.22528, 0.191628, 5.63326, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.000512437, 0.0176018, 0.225236, 0.14026, 0.304261, 1.60256, 1.11084, 0.173355, 5.07615, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.000897641, 0.0537124, 0.966802, 0.72113, 6.35905, 30.1998, 23.9929, 2.69325, 40.7497, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.000557466, 0.115691, 1.47457, 1.42752, 11.3666, 38.3024, 35.6621, 4.19459, 38.2547, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00189842, 0.539183, 16.0415, 12.1554, 50.3037, 86.4773, 57.669, 14.8169, 81.1911, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00364662, 2.93012, 99.1684, 67.4182, 175.598, 226.082, 56.3963, 48.0486, 134.506, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0167907, 177.705, 884.861, 265.04, 346.967, 347.699, 74.8514, 96.9826, 252.722, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.103497, 1461.4, 4819.42, 665.406, 962.257, 761.05, 144.923, 91.3213, 251.49, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.597037, 989.317, 2421.98, 450.242, 695.759, 608.378, 195.45, 80.5629, 242.759, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.57815, 190.965, 905.128, 450.0, 975.852, 812.193, 263.317, 65.2961, 287.169, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.21458, 192.572, 3683.69, 2185.01, 3129.27, 3324.73, 682.884, 292.513, 342.247, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.941099, 756.786, 5932.71, 9509.85, 11564.5, 7490.03, 908.063, 431.368, 230.316, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.695599, 154.726, 1868.16, 3996.22, 3776.84, 3483.44, 774.084, 86.672, 81.2929, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.03262, 187.96, 1915.83, 2307.07, 3046.11, 3802.32, 2348.24, 203.306, 59.4469, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][9.50691, 313.284, 10416.8, 65536.4, 1.07941e5, 87557.8, 18107.3, 1430.34, 216.158, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][51.7566, 1371.62, 41612.7, 1.47855e5, 1.51472e5, 1.04217e5, 76885.2, 4816.93, 340.386, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][210.823, 8231.6, 1.62499e5, 231319.0, 88519.3, 97615.1, 82771.0, 5440.72, 206.668, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][218.149, 23801.8, 2.28332e5, 2.52207e5, 1.42658e5, 110985.0, 50656.9, 3131.84, 201.46, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][153.417, 14108.9, 82403.9, 80701.0, 39533.2, 22814.5, 7877.38, 1395.02, 99.321, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1041.21, 28848.6, 2.30035e5, 2.77206e5, 183462.0, 89626.2, 30172.2, 5143.68, 290.232, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1321.79, 12513.0, 91287.2, 123139.0, 121958.0, 81111.1, 58270.9, 13737.7, 703.333, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1492.39, 9941.57, 1.15193e5, 1.21051e5, 68036.9, 36373.8, 18025.3, 4905.59, 864.767, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][5080.73, 24115.3, 84736.5, 77431.4, 59246.7, 46812.6, 32761.9, 10902.4, 2086.45, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][10111.8, 44851.4, 84040.6, 37042.3, 23928.1, 16076.3, 14003.1, 5287.24, 1030.28, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][9922.03, 1.68531e5, 2.23398e5, 57913.1, 41517.2, 43663.9, 60130.1, 24591.4, 3234.95, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
191[0.0770436, 0.00820453, 0.00144554, 0.0066907, 0.143037, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.115118, 0.00808703, 0.00118068, 0.0132742, 0.0605214, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0465763, 0.00327199, 0.000477701, 0.00537071, 0.0244868, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0835599, 0.00879598, 0.00353332, 0.0178166, 0.0500842, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0748962, 0.00791888, 0.00319084, 0.0160918, 0.0453652, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.21166, 0.0583619, 0.0370389, 0.555883, 1.31096, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.24531, 0.147559, 0.0718265, 2.51977, 7.36074, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][21.7611, 2.07488, 0.352261, 12.5853, 35.656, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][132.065, 9.2601, 1.13391, 22.8247, 52.2725, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][266.73, 16.257, 1.64042, 8.93951, 15.2865, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][313.677, 47.0178, 3.38845, 5.81448, 24.1833, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][188.16, 70.4416, 7.306, 25.6472, 161.155, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][502.634, 101.855, 14.3696, 34.0735, 162.943, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][627.645, 185.123, 77.6637, 96.1907, 1032.13, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1209.68, 389.994, 184.43, 155.859, 477.934, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4343.79, 849.577, 327.416, 164.026, 260.743, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][6774.72, 1781.12, 946.655, 632.797, 443.285, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][17237.7, 11026.6, 3579.41, 2186.11, 962.677, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][14077.7, 6869.17, 3030.34, 2785.97, 1431.79, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][69073.6, 27237.0, 8487.33, 13268.1, 12012.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.60968e5, 1.58409e5, 32785.7, 21847.4, 11701.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.30748e5, 62570.8, 22554.0, 14135.6, 7167.4, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.03554e6, 279403.0, 10362.9, 4918.85, 2157.49, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][6.14458e5, 1.31865e5, 14703.7, 6879.12, 3759.23, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][6.28425e5, 1.57054e5, 21824.9, 11577.3, 6606.75, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.28999e6, 4.54985e5, 95437.3, 40280.6, 10591.9, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.04243e6, 8.30455e5, 1.13747e5, 53298.6, 19648.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.46318e6, 1.15275e6, 2.17709e5, 1.04344e5, 35618.9, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
192[0.0453022, 0.00469916, 0.00193911, 0.00619609, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0162656, 0.00264962, 0.000846998, 0.00225862, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00658101, 0.00107203, 0.000342693, 0.000913833, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0234711, 0.00574718, 0.00662632, 0.00835067, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0212056, 0.00521154, 0.00601776, 0.00751325, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.277803, 0.119607, 0.156052, 0.053769, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.570449, 0.24573, 0.250681, 0.0234114, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.1693, 0.684178, 0.406613, 0.281151, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][30.4787, 2.04267, 0.580596, 1.28702, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][151.663, 7.6201, 2.02173, 10.1178, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][279.249, 9.12853, 4.98589, 363.369, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][434.595, 13.0439, 8.40123, 842.283, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][779.377, 25.347, 12.9338, 51.5342, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1461.63, 72.0392, 34.5911, 25.8889, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2557.94, 389.613, 100.856, 561.311, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3241.37, 253.953, 77.4396, 93.1323, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3451.06, 113.911, 64.3423, 49.088, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2958.34, 850.289, 428.186, 297.715, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][5845.54, 6450.45, 4776.78, 2419.67, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][6953.96, 6062.52, 2393.43, 949.55, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][13091.0, 5575.42, 1317.53, 268.897, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][45203.9, 3263.63, 1212.38, 308.828, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.30112e5, 23305.2, 7908.53, 1878.7, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.20449e6, 69176.3, 24712.6, 6995.91, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][8.88015e5, 1.11023e5, 66709.8, 24834.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.2419e5, 42421.8, 25138.0, 12903.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.19886e6, 296121.0, 1.77641e5, 68981.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][9.95061e5, 2.64532e5, 1.39998e5, 36914.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
193[3.23477e-5, 0.000132317, 0.000143602, 0.000385296, 0.0215862, 0.0367591, 0.00904464, 0.0214649, 0.0223188, 0.0445251, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.90018e-5, 7.08086e-5, 6.93151e-5, 0.000174685, 0.00977338, 0.0182157, 0.00556471, 0.0112506, 0.00797403, 0.0179365, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][7.68809e-6, 2.8649e-5, 2.80447e-5, 7.06772e-5, 0.00395429, 0.00737002, 0.00225147, 0.00455199, 0.00322627, 0.00725706, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.43774e-5, 5.66218e-5, 5.04716e-5, 0.000131138, 0.0189074, 0.0275439, 0.00369431, 0.0232008, 0.0107908, 0.0421967, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.19049e-5, 5.08832e-5, 4.53279e-5, 0.000117901, 0.0169801, 0.0247473, 0.00332262, 0.0210107, 0.00975862, 0.0388348, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][8.83781e-5, 0.00023037, 0.000169713, 0.000539092, 0.058158, 0.0960804, 0.0224997, 0.411744, 0.263369, 3.41234, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.62514e-5, 0.000200982, 0.000134938, 0.000430639, 0.063493, 0.182518, 0.0912318, 1.08382, 1.0819, 11.9177, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.000103273, 0.000404948, 0.000274813, 0.000937404, 0.257372, 1.89393, 1.1815, 3.19392, 3.72564, 32.2762, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.000184391, 0.000538545, 0.000336535, 0.0016643, 0.419372, 15.1084, 3.6744, 5.98198, 6.36828, 26.0508, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.000177705, 0.000342752, 0.000490615, 0.00321954, 11.6373, 100.881, 8.70401, 32.923, 29.8845, 28.6337, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.000415825, 0.000582552, 0.000951629, 0.00473497, 281.356, 504.356, 96.517, 256.625, 198.4, 107.618, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00223301, 0.00271011, 0.00119407, 0.011139, 470.871, 779.663, 227.49, 338.36, 215.611, 159.88, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00704403, 0.0107172, 0.00386897, 0.0334865, 196.809, 382.443, 174.591, 234.25, 60.7561, 107.774, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0106445, 0.0163779, 0.0159694, 0.053589, 358.278, 708.621, 339.214, 1216.43, 742.185, 307.586, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0772909, 0.0400303, 0.0518045, 0.158629, 4794.6, 6330.37, 2014.74, 2887.57, 2508.66, 834.672, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.64917, 0.0486712, 0.0938011, 0.55512, 7265.83, 8786.45, 1726.27, 656.095, 426.954, 261.586, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][10.5364, 0.449329, 0.628115, 2.7933, 2907.51, 4041.71, 706.441, 488.276, 705.748, 701.672, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][36.6246, 6.27074, 8.75925, 7.77679, 3337.2, 8192.7, 7062.31, 7814.3, 8183.67, 3139.46, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][73.2888, 37.6893, 43.6769, 74.8723, 7128.33, 26188.5, 81195.3, 84234.1, 28638.1, 4970.37, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][265.342, 210.527, 213.159, 285.278, 57736.8, 65156.1, 1.0981e5, 1.09415e5, 33790.1, 10745.8, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][873.293, 400.718, 305.769, 138.677, 57824.3, 89242.9, 136367.0, 73705.5, 13144.4, 4092.97, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3554.55, 725.404, 369.183, 87.2091, 7920.96, 55770.3, 59948.6, 28816.3, 12110.5, 2144.29, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][7567.87, 2079.56, 1732.32, 896.754, 1.19794e5, 2.72341e5, 1.40145e5, 86443.0, 32849.9, 12704.6, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][29043.6, 4201.58, 1844.2, 317.008, 56289.6, 1.20801e5, 1.42342e5, 1.39142e5, 54506.0, 5538.42, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][48873.7, 4502.98, 1998.61, 268.973, 5685.12, 90631.4, 1.4876e5, 1.21371e5, 46534.0, 3494.68, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][104274.0, 10275.3, 2506.55, 347.27, 37942.1, 3.37393e5, 4.44968e5, 1.54717e5, 26568.5, 4696.19, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][87503.6, 11795.1, 4269.91, 695.911, 1.73919e5, 1.01668e6, 2.19081e6, 1.91798e6, 5.91536e5, 58624.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.00358e5, 10162.7, 4837.1, 4468.57, 1.7343e5, 1.12697e6, 1.79611e6, 1.90568e6, 9.97478e5, 1.26941e5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
194[0.127782, 0.101379, 0.0369538, 0.019505, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.136504, 0.0900751, 0.0530071, 0.0228197, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.055229, 0.0364442, 0.0214465, 0.00923281, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0857668, 0.050691, 0.0177172, 0.0138828, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0770652, 0.0456759, 0.0159742, 0.0125029, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.397199, 0.427606, 0.173895, 0.0859272, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.42625, 1.60168, 0.622152, 0.213186, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][7.69097, 9.78797, 2.45688, 0.72708, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][63.3174, 87.3017, 17.9911, 1.91962, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][660.468, 570.865, 163.819, 25.5927, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1802.46, 1158.36, 497.111, 107.694, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][708.735, 304.583, 166.545, 43.8995, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][786.342, 486.603, 159.533, 48.3609, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3081.43, 2125.19, 2227.71, 1208.11, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][15262.5, 13128.3, 14669.3, 9959.21, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][6904.68, 11595.0, 11359.8, 6384.05, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][14255.3, 20089.4, 16443.4, 7090.37, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][20155.8, 20658.7, 13539.2, 7993.09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][13078.0, 20410.0, 23110.1, 15057.7, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][49378.3, 48825.6, 1.25274e5, 59399.8, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][55320.9, 1.45795e5, 2.05762e5, 93083.9, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][46462.8, 77472.0, 81888.6, 21503.9, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.80606e5, 3.13232e5, 3.39605e5, 1.27875e5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.66725e5, 2.34534e5, 2.99865e5, 1.65914e5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2.70836e5, 3.18779e5, 3.70377e5, 1.86439e5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.58919e5, 4.32605e5, 3.79268e5, 2.25451e5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][7.83102e5, 8.42117e5, 6.41037e5, 2.91679e5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.4574e6, 3.11895e6, 3.26029e6, 1.17651e6, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
195[0.00149723, 0.000397901, 0.0010245, 0.17157, 0.276365, 0.0568549, 0.0536703, 0.439603, 0.599519, 0.126497, 0.00765833, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.000619492, 0.000181285, 0.000723292, 0.162552, 0.357302, 0.139281, 0.0253212, 0.291274, 0.288937, 0.064765, 0.00581977, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.000250645, 7.33474e-5, 0.000292642, 0.0657682, 0.144563, 0.0563528, 0.0102449, 0.117849, 0.116903, 0.0262038, 0.00235467, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.000373739, 0.000199805, 0.000366983, 0.098853, 0.360346, 0.22644, 0.027896, 0.675366, 0.782904, 0.128503, 0.0192739, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.000336269, 0.000179765, 0.000329724, 0.0889074, 0.32451, 0.20409, 0.0251495, 0.608854, 0.706478, 0.116744, 0.017413, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00199025, 0.00100767, 0.00138487, 0.478619, 2.71661, 2.21372, 0.28749, 5.34833, 7.93666, 3.54475, 0.26917, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0033065, 0.00073877, 0.00147344, 0.313357, 4.65791, 5.52156, 0.960435, 4.16268, 12.1532, 12.2444, 0.925876, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0103874, 0.00164283, 0.00306121, 1.0687, 39.1471, 45.7576, 6.41357, 81.6527, 119.201, 52.599, 5.67519, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0123423, 0.00310495, 0.00510657, 15.3814, 315.57, 298.942, 30.0513, 1217.55, 1630.99, 167.131, 18.5235, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00773095, 0.00471321, 0.00931801, 168.107, 2144.02, 1206.5, 104.362, 5122.19, 6191.16, 551.797, 47.8003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.014134, 0.0123707, 0.0167875, 406.073, 2981.5, 1004.94, 127.551, 2277.57, 2870.24, 607.262, 40.7236, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0613332, 0.081441, 0.0673037, 146.917, 431.665, 284.66, 143.553, 126.79, 1301.4, 896.056, 32.5432, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.22471, 0.228731, 0.228438, 120.682, 265.257, 210.256, 113.583, 163.597, 1632.43, 456.451, 27.539, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.00315, 0.481759, 0.409897, 507.07, 1119.07, 1373.77, 3250.93, 1706.53, 879.379, 317.436, 24.7567, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][11.9272, 4.52922, 3.14836, 6346.03, 8032.54, 26480.4, 33573.7, 6904.11, 11211.6, 6473.83, 40.6373, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.75794, 1.9829, 1.91324, 911.475, 1691.29, 1656.45, 975.606, 652.946, 2852.51, 1817.45, 52.6666, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.82994, 1.83739, 1.8792, 1044.49, 3294.7, 2732.07, 2005.99, 3829.05, 3666.24, 780.573, 99.4934, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][6.79328, 6.56466, 6.17797, 2746.58, 10828.8, 18963.6, 29276.8, 17209.1, 7385.64, 1544.29, 26.7564, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][20.7357, 22.6489, 19.6382, 5925.78, 10156.3, 26737.3, 31352.8, 12791.2, 8443.78, 2117.69, 56.2061, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][122.102, 237.833, 170.211, 21403.2, 49907.8, 50456.1, 76891.4, 70109.0, 64494.8, 28382.6, 423.936, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][677.617, 817.882, 508.911, 27824.1, 1.29543e5, 1.21293e5, 2.72558e5, 1.73446e5, 100057.0, 46003.6, 1259.14, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][351.757, 436.467, 284.264, 9104.04, 55924.2, 71568.0, 46204.7, 26932.3, 28671.7, 8351.16, 111.886, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][174.842, 219.985, 213.321, 5674.75, 73477.7, 1.02485e5, 79516.6, 45339.3, 28572.8, 6551.63, 375.731, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2264.71, 1685.51, 2243.32, 23492.7, 2.91868e5, 4.09801e5, 2.87919e5, 1.59223e5, 1.02448e5, 26992.2, 1149.19, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][2459.21, 2286.52, 2511.81, 45982.5, 2.5487e5, 3.08495e5, 1.80253e5, 1.25295e5, 98768.4, 26979.9, 751.298, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][701.548, 984.096, 865.57, 13528.7, 1.07505e5, 1.55366e5, 99258.1, 47461.9, 36128.9, 8840.69, 195.162, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][750.569, 1060.96, 616.738, 31305.8, 187821.0, 3.06493e5, 2.84938e5, 1.06541e5, 41605.1, 1705.17, 242.721, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1625.48, 1670.15, 1026.61, 5.26785e5, 1.21928e6, 8.63865e5, 8.16701e5, 5.27941e5, 433695.0, 15172.9, 869.901, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
196[0.00252365, 0.0540424, 0.0652368, 0.019338, 0.0124232, 0.00385076, 0.00511448, 0.00346474, 0.00342869, 0.0238765, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00247622, 0.117222, 0.19843, 0.0274702, 0.0143665, 0.00181369, 0.00400859, 0.00402005, 0.00280431, 0.0134033, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00100187, 0.0474279, 0.0802844, 0.0111144, 0.00581265, 0.000733817, 0.00162187, 0.0016265, 0.00113462, 0.00542295, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00208061, 0.293333, 0.323671, 0.0339522, 0.0197604, 0.00237492, 0.00197823, 0.00127686, 0.00112395, 0.0126247, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00186535, 0.265451, 0.291843, 0.0305672, 0.0177951, 0.00213975, 0.00178165, 0.00114981, 0.00101206, 0.0113768, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00492873, 4.80054, 3.60443, 0.240727, 0.170299, 0.025086, 0.0201474, 0.00914002, 0.00784018, 0.0892741, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.00972581, 8.83869, 7.23492, 0.303484, 0.261153, 0.0659352, 0.0513253, 0.0313255, 0.021287, 0.104359, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0218923, 19.243, 17.2961, 0.834671, 0.56984, 0.148268, 0.0825495, 0.0411887, 0.0424503, 0.237966, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0195735, 25.5809, 25.8381, 2.18252, 1.21303, 0.238115, 0.0512912, 0.0227053, 0.0416166, 0.426058, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.022393, 24.2565, 37.9967, 4.55617, 2.96319, 0.464506, 0.0792859, 0.0398073, 1.54631, 4.54765, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0242251, 69.0934, 124.723, 13.4178, 5.22177, 0.445136, 0.141627, 0.0893576, 13.5238, 93.0443, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0747583, 345.824, 436.331, 43.3585, 8.52414, 1.57341, 0.389083, 0.3087, 10.7385, 158.487, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.31791, 566.411, 719.382, 118.199, 32.2727, 7.10288, 1.58353, 1.38016, 1.42206, 16.0136, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.92624, 568.99, 575.37, 156.396, 119.329, 59.0076, 17.0401, 39.5008, 34.8245, 85.2229, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.65574, 10243.4, 12315.3, 2227.61, 664.239, 1288.62, 1169.92, 1786.39, 1022.97, 1355.31, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][14.4501, 63891.1, 60466.1, 16105.7, 6109.97, 15921.7, 20731.0, 15994.0, 1746.19, 152.261, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][7.78462, 44738.3, 48691.6, 34519.9, 28750.4, 22145.2, 15343.5, 5603.77, 82.1619, 74.8241, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][13.9255, 15193.9, 42657.8, 63297.8, 58052.9, 60195.8, 38842.6, 4183.23, 134.844, 44.5372, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.37215, 11064.0, 24972.2, 74081.4, 1.08492e5, 48681.4, 11018.6, 2674.41, 218.69, 64.4355, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][7.89324, 13071.2, 21931.0, 11973.5, 15418.0, 16936.2, 19673.5, 10221.3, 273.744, 105.865, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][33.6375, 28828.3, 33827.7, 28803.7, 38635.5, 43586.0, 36909.5, 11885.3, 1286.47, 176.552, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][307.146, 95475.7, 1.17413e5, 1.13743e5, 1.31387e5, 94663.6, 46113.3, 12007.0, 2734.88, 365.088, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][482.278, 3.51068e5, 3.88906e5, 4.75666e5, 5.75415e5, 3.11883e5, 1.4039e5, 49555.4, 4164.32, 915.903, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][615.394, 3.92805e5, 5.17524e5, 7.68245e5, 1.02471e6, 5.52293e5, 2.39684e5, 86537.2, 6650.66, 1240.86, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][7578.1, 1.8436e6, 2.73977e6, 2.97279e6, 2.26203e6, 1.81251e6, 1.55859e6, 358331.0, 35307.1, 2508.01, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][25244.4, 5.07954e6, 1.31796e7, 1.40058e7, 1.27597e7, 8.51875e6, 5.15378e6, 2.10335e6, 3.92957e5, 29356.9, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][13622.8, 1.71869e6, 2.50539e6, 1.53882e6, 1.39828e6, 8.68007e5, 5.75198e5, 1.91021e5, 26860.6, 2693.17, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4551.63, 8.1109e5, 1.22325e6, 690890.0, 6.51636e5, 3.50233e5, 186925.0, 57849.3, 6157.3, 588.89, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
197[0.115361, 0.0464483, 0.0123202, 0.0632743, 0.11675, 0.0424258, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.206398, 0.0766185, 0.0210895, 0.0674126, 0.107959, 0.0308161, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0835083, 0.0309996, 0.00853277, 0.027275, 0.0436798, 0.0124681, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.234684, 0.0745736, 0.0204655, 0.0366456, 0.0704176, 0.0359, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.211086, 0.0670677, 0.0184346, 0.0328961, 0.0632762, 0.0323052, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.12866, 0.355707, 0.136239, 0.111711, 0.28501, 0.232529, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.674157, 0.514101, 0.252998, 0.168851, 0.338446, 0.301313, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.546261, 1.26355, 0.798744, 0.419339, 1.39225, 1.44767, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.93425, 1.43249, 1.46607, 1.12628, 3.72256, 16.325, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][34.3193, 1.94558, 1.86993, 11.4348, 141.679, 273.495, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][746.442, 10.086, 2.40589, 232.759, 1884.17, 1262.68, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3768.57, 46.7528, 1.98855, 6176.14, 9678.99, 692.608, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][957.84, 18.6519, 3.23436, 7440.54, 7997.95, 537.632, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][73.2896, 8.6314, 3.62732, 178.192, 1170.35, 3213.71, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][406.588, 3.68579, 1.51439, 24.9124, 4331.24, 3371.67, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][272.894, 6.17965, 1.70592, 170.465, 942.132, 272.696, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][881.39, 52.3759, 47.8773, 161.74, 3672.64, 1841.64, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][9634.62, 3250.83, 1437.82, 15526.1, 29398.7, 6510.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][7891.22, 3483.18, 338.92, 4682.33, 15818.6, 6142.17, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3080.29, 1461.23, 893.893, 2698.82, 5878.18, 1772.11, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][61562.9, 42404.1, 19231.4, 13520.2, 21887.5, 4165.85, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][60104.9, 14105.5, 3402.71, 7270.35, 9808.96, 1492.81, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][93530.2, 1429.72, 646.662, 4840.68, 6426.18, 1497.02, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.37752e5, 3209.86, 476.808, 750.046, 1060.53, 242.128, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][4.07255e5, 5381.54, 631.243, 1725.49, 2653.75, 442.006, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][1.22697e5, 1595.19, 344.311, 1009.06, 1046.03, 121.785, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][3.67178e5, 4340.25, 438.249, 362.808, 339.1, 39.2968, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0][18475.8, 1058.32, 527.914, 1346.66, 2348.97, 732.023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
In [26]:
names(X1_df)
Out[26]:
30-element Vector{String}:
 "cough_F1"
 "cough_F2"
 "cough_F3"
 "cough_F4"
 "cough_F5"
 "cough_F6"
 "cough_F7"
 "cough_F8"
 "cough_F9"
 "cough_F10"
 "cough_F11"
 "cough_F12"
 "cough_F13"
 ⋮
 "cough_F19"
 "cough_F20"
 "cough_F21"
 "cough_F22"
 "cough_F23"
 "cough_F24"
 "cough_F25"
 "cough_F26"
 "cough_F27"
 "cough_F28"
 "cough_F29"
 "cough_F30"
In [39]:
# Let's inspect some instances
plot(map(i->plot(collect(X1_df[i,:]), labels=nothing,title=y[i]), 1:35:(35*6))..., layout = (2, 3), size = (1500,400))
Out[39]:
In [41]:
# All instances, grouped by class
plot(map((((X_mod, mod_name), _y),)->plot(collect.(eachrow(X_mod[findall(__y->__y == _y, y),:])), labels=nothing,title="$(_y) $(mod_name)"), Iterators.product(zip(eachmodality(X_multimodal), ["cough", "breath"]), unique(y)))..., layout = (2, 2), size = (1500,400))
Out[41]:
In [72]:
using ModalDecisionTrees
Out[72]:
untrained Machine; caches model-specific representations of data
  model: ModalDecisionTree(max_depth = nothing, …)
  args: 
    1:	Source @567 ⏎ Table{AbstractVector{AbstractVector{Continuous}}}
    2:	Source @759 ⏎ AbstractVector{Textual}
In [ ]:
# Train in cross-validation!
e = evaluate!(machine(ModalDecisionTree(; relations = :RCC8), X_multimodal, y);
        resampling=StratifiedCV(shuffle=true, nfolds = 3),
        measures=[accuracy],
        verbosity=0,
        check_measure=false
)
[ Info: Precomputing logiset...
In [ ]:
# Accuracies per fold
e.per_fold
In [71]:
e.report_per_fold[2].solemodel
Out[71]:
▣ {1}(⟨G⟩(min[V31] ≥ 0.001853897887096119))
├✔ {1}(⟨G⟩((min[V31] ≥ 0.001853897887096119) ∧ ⟨A̅O̅⟩(min[V27] < 76685.17720224746)))
│├✔ {1}(⟨G⟩((min[V31] ≥ 0.001853897887096119) ∧ ⟨A̅O̅⟩((min[V27] < 76685.17720224746) ∧ (min[V28] < 44762.952262639636))))
││├✔ {1}(⟨G⟩((min[V31] ≥ 0.001853897887096119) ∧ ⟨A̅O̅⟩((min[V27] < 76685.17720224746) ∧ (min[V28] < 44762.952262639636) ∧ ⟨D̅B̅E̅⟩(min[V50] ≥ 1885.5712367271199))))
│││├✔ {1}(⟨G⟩((min[V31] ≥ 0.001853897887096119) ∧ ⟨A̅O̅⟩((min[V27] < 76685.17720224746) ∧ (min[V28] < 44762.952262639636) ∧ ⟨D̅B̅E̅⟩((min[V50] ≥ 1885.5712367271199) ∧ (min[V13] ≥ 1.400957923736261)))))
││││├✔ NEGATIVE
││││└✘ POSITIVE
│││└✘ NEGATIVE
││└✘ POSITIVE
│└✘ NEGATIVE
└✘ {1}(⟨G⟩(min[V27] ≥ 2.170219509362793e6))
 ├✔ {1}(⟨G⟩((min[V27] ≥ 2.170219509362793e6) ∧ ⟨G⟩(min[V46] ≥ 5838.390775457752)))
 │├✔ POSITIVE
 │└✘ {1}(⟨G⟩((min[V27] ≥ 2.170219509362793e6) ∧ (min[V19] ≥ 30000.48907253628)))
 │ ├✔ NEGATIVE
 │ └✘ {1}(⟨G⟩((min[V27] ≥ 2.170219509362793e6) ∧ (min[V21] < 20414.774427686534)))
 │  ├✔ NEGATIVE
 │  └✘ POSITIVE
 └✘ {1}(⟨G⟩(min[V28] ≥ 553537.8712413169))
  ├✔ POSITIVE
  └✘ {1}(⟨G⟩(min[V2] ≥ 0.17083754207872534))
   ├✔ {1}(⟨G⟩((min[V2] ≥ 0.17083754207872534) ∧ (min[V11] ≥ 1108.1113127342035)))
   │├✔ NEGATIVE
   │└✘ POSITIVE
   └✘ NEGATIVE

In [46]:
report(mach).solemodel
Out[46]:
▣ {1}(⟨G⟩(min[V37] ≥ 0.0013205573259328035))
├✔ {1}(⟨G⟩((min[V37] ≥ 0.0013205573259328035) ∧ ⟨L̅⟩(min[V27] ≥ 226321.9912113276)))
│├✔ NEGATIVE
│└✘ {1}(⟨G⟩((min[V37] ≥ 0.0013205573259328035) ∧ (min[V48] ≥ 1242.1904769961468)))
│ ├✔ {1}(⟨G⟩((min[V37] ≥ 0.0013205573259328035) ∧ (min[V48] ≥ 1242.1904769961468) ∧ ⟨AO⟩(min[V40] ≥ 3.51978641624239)))
│ │├✔ {1}(⟨G⟩((min[V37] ≥ 0.0013205573259328035) ∧ (min[V48] ≥ 1242.1904769961468) ∧ ⟨AO⟩((min[V40] ≥ 3.51978641624239) ∧ ⟨AO⟩(min[V31] ≥ 1.6207745800042226e-5))))
│ ││├✔ POSITIVE
│ ││└✘ NEGATIVE
│ │└✘ POSITIVE
│ └✘ NEGATIVE
└✘ {1}(⟨G⟩(min[V27] ≥ 2.170219509362793e6))
 ├✔ {1}(⟨G⟩((min[V27] ≥ 2.170219509362793e6) ∧ ⟨G⟩(min[V46] ≥ 5838.390775457752)))
 │├✔ POSITIVE
 │└✘ {1}(⟨G⟩((min[V27] ≥ 2.170219509362793e6) ∧ (min[V30] < 1.6492884918659376e6)))
 │ ├✔ POSITIVE
 │ └✘ NEGATIVE
 └✘ {1}(⟨G⟩(min[V28] ≥ 672777.1743629333))
  ├✔ POSITIVE
  └✘ {1}(⟨G⟩(min[V30] ≥ 1.0114283593133552e6))
   ├✔ NEGATIVE
   └✘ POSITIVE

In [ ]:
X = scalarlogiset(X_df)
println(X)
In [ ]:

In [ ]:
# Accessibles on multirelation frames
# Get the structure ("frame") of the first instance. It is a "dimensional" frame, of all interval from 1 to 51.
fr = SoleLogics.frame(X, 1)
In [ ]:
# Enumerate all worlds
collect(allworlds(fr))
In [ ]:
using SoleLogics: Interval
# Enumerate the intervals that are "Later" than [1,10]
accessibles(fr, Interval(1,10), IA_L) |> collect
In [ ]:
# Remember that features are computed on each world
# Let's compute the minimum of the first variable on an arbitrary interval, that is, "X[Hand tip l]".
feature = UnivariateMin(1)
Sole.featvalue(feature, X, 1, Interval(10,30))
In [ ]:
# Remember that atoms are *scalar conditions on features*
# Let's check one on an interval of the first instance
p = Atom(ScalarCondition(feature, >, -0.5))
check(p, X, 1, Interval(10,30))
In [ ]:
# I can check any formula
p = Atom(ScalarCondition(UnivariateMin(1), >, -0.5))
q = Atom(ScalarCondition(UnivariateMin(2), <=, 10))
φ = p ∨ q
check(φ, X, 1, Interval(10,30))
In [ ]:
# Generate a random HS formula with scalar conditions on features, and check it on the dataset.
features = [UnivariateMin(i_variable) for i_variable in 1:ncol(X_df)]
alpha = [Atom(ScalarCondition(feat, >, thresh)) for feat in features for thresh in 0:0.1:1]

HS_connectives = SoleLogics.diamondsandboxes(SoleLogics.IARelations)
propo_connectives = SoleLogics.BASE_PROPOSITIONAL_CONNECTIVES

println("Propositional connectives: $(join(syntaxstring.(propo_connectives), ", "))")
println("HS connectives: $(join(syntaxstring.(HS_connectives), ", "))")

propo_weights = fill(1/length(propo_connectives), length(propo_connectives))
HS_weights = fill(1/length(HS_connectives), length(HS_connectives))

connectives = vcat(propo_connectives, IA_connectives)

opweights = vcat(propo_weights, HS_weights)
    
treeheight = 3
φ2 = randformula(Random.MersenneTwister(30), treeheight, alpha, connectives; opweights = opweights)
println()
println("Random formula:")
println(syntaxstring(φ2))
        
check(φ2, X, 1, Interval(10,30))
In [ ]:
# Let's check a formula on all the instances
check_mask = check(φ2, X, Interval(10,30))
In [ ]:
# It holds on part of the instances
sum(check_mask)
In [ ]:
# Let's ask whether the formula holds *all* intervals, instead of checking it on [1,2]
println("Applying the universal global operator: ", SoleLogics.globalbox)
println()

universal_φ = globalbox(φ2)
println("Formula: ", syntaxstring(universal_φ))
check_mask = check(universal_φ, X)

# It holds on no instance... Too restrictive!
sum(check_mask)
In [ ]:
# Let's ask whether there exists any interval where the formula holds
println("Applying the existential global operator: ", SoleLogics.globaldiamond)
println()

existential_φ = globaldiamond(φ2)
println("Formula: ", syntaxstring(existential_φ))
check_mask = check(existential_φ, X)

# It holds on more instances
sum(check_mask)
In [ ]:
# Question: does it lead to a good rule?

println(syntaxstring(existential_φ))

println()
println(SoleLogics.experimentals.formula2natlang(existential_φ))
In [ ]:
neg_existential_φ = normalize(¬ existential_φ;
    profile = :readability,
    remove_implications = true,
    allow_atom_flipping = true
)

syntaxstring(neg_existential_φ; remove_redundant_parentheses = false)
In [ ]:
(SoleLogics.precedence(∧), SoleLogics.precedence(∨))
In [ ]:
countmap(y)
In [ ]:
println(existential_φ)
countmap(y[check_mask])
In [ ]:
println(neg_existential_φ)
countmap(y[(!).(check_mask)])
In [ ]:
branch = Branch(neg_existential_φ, "I have command", "Spread wings")
In [ ]:
y_preds = SoleModels.apply(branch, X)
println("Accuracy of this branch: $(sum(y .== y_preds)/length(y))")
println("Random chanc e: $(60/length(y))")
In [ ]:

In [ ]:
println(X)
In [ ]:
# Randomly split the data: 20% training, 80% testing
N = nrow(X_df)
perm = randperm(Random.MersenneTwister(1), N)
train_idxs, test_idxs = perm[1:round(Int, N*.2)], perm[round(Int, N*.2)+1:end];
println("Using $(length(train_idxs)) instances for training")
println("Using $(length(test_idxs)) instances for testing")
In [ ]:
using ModalDecisionTrees

# Bind a machine learning algorithm to logiset & labels
mach = machine(ModalDecisionTree(; relations = :IA7, features = [minimum]), X_df, y)

# Train!
@time fit!(mach; rows=train_idxs);

# Compute accuracy
yhat = predict_mode(mach; rows=test_idxs)
MLJ.accuracy(yhat, y[test_idxs])
In [ ]:
# Show the restricted MDT learnt
printmodel(report(mach).rawmodel_full; hidemodality = true)
In [ ]:
# Show its *pure* version
printmodel(report(mach).solemodel_full; show_metrics = true, hidemodality = true)
In [ ]:
simplified_restricted_tree = ModalDecisionTrees.prune(report(mach).rawmodel_full; simplify = true)
printmodel(simplified_restricted_tree)

println()
println("# Leaves: ", nleaves(simplified_restricted_tree))
In [ ]:
solemodel = ModalDecisionTrees.translate(simplified_restricted_tree)
In [ ]:
# Print leaf rules + their training performances
ruleset = listrules(solemodel)
printmodel.(ruleset; show_metrics = true, threshold_digits = 2, variable_names_map = [names(X_df)],parenthesize_atoms = false, hidemodality = true);
In [ ]:
last_rule = ruleset[end]
last_antd = antecedent(last_rule)

println("First formula, translated:")
println(SoleLogics.experimentals.formula2natlang(last_antd; threshold_digits = 2, use_feature_abbreviations = true))
    

for (i_rule, rule) in enumerate(ruleset)
    println()
    println("[$i_rule]")
    antd = antecedent(rule)
    println(SoleLogics.experimentals.formula2natlang(antd; threshold_digits = 2, use_feature_abbreviations = true), "\n");
end
In [ ]:
# Print rules + their *test* performances

# Sprinkle the model with the test instances!
predictions, tree_test = report(mach).sprinkle(X_df[test_idxs,:], y[test_idxs]; simplify = true);

# Extract ruleset and print its metrics
ruleset_test = listrules(tree_test);

# printmodel.(ruleset_test; show_metrics = true, threshold_digits = 2, variable_names_map = [names(X_df)], parenthesize_atoms = true, hidemodality = true);
printmodel.(ruleset_test; show_metrics = true, threshold_digits = 2, parenthesize_atoms = false, hidemodality = true);
In [ ]:
println("IF\n\t", SoleLogics.experimentals.formula2natlang(antecedent(ruleset_test[4])))
println("THEN\n\t", consequent(ruleset_test[4]))
In [ ]:
# Obtain class rules & show their *test* metrics
condensed_ruleset_test = joinrules(ruleset_test)
printmodel.(condensed_ruleset_test; show_metrics = true, threshold_digits = 2, parenthesize_atoms = false, hidemodality = true);

Exercise¶

ModalDecisionTrees.jl can also handle images! In which case, they use a 2D logic of rectangles instead of a 1D logic of intervals.

Apply ModalDecisionTrees to Indian Pines, a benchmark dataset for Land Cover Classification with 16 classes. The dataset consists of a hyperspectral image (i.e., 200 color channels instead of the typical 3 RGB channels) where many pixels have been labelled as belonging to one of the classes.

Sketch of the idea:

  • Load the image and the ground truths. The package MAT.jl can be helpful;
  • From the $145 \times 145$ image provided, sample a (small) number $m$ of $3 \times 3$ patches for each class, and label each patch with the class label for the central pixel;
  • Gather the ground truths into a vector of strings y, and the samples into a Julia DataFrame X with 200 columns, $16m$ rows and $3 \times 3$ matrices in the cells;
  • Use MLJ to train a ModalDecisionTree on X and y, similarly to the above case.

Suggestion: since the formulas are desirably rotation-invariant, ask the algorithm to use topological relations instead of directional relations. Rrefer to the doc to know more.